Price vs Quantity: The Showdown of Oligopolies

January 25, 2018

Many economics students you would talk to would be familiar with the Cournot and Bertrand models of competition. It’s one of the main things learnt in any industrial module or intermediate microeconomics course, encompassing duopolistic competition with the infamous Nash equilibrium – it’s a key industrial concept that highlights the differences between quantity and price competition in a simple duopoly or oligopoly, which are the firms that lead and dominate certain markets.

In a nutshell, the Cournot model describes industry structure where firms compete solely on the output they product – in order to produce its mathematically sound outcome, the model relies on several key assumptions, such as no product differentiation and profit maximisation. The outcome of the Cournot model implies, for the most part, positive profits for two firms in a duopoly – when the number of firms increases, we find that the model effectively becomes a model of perfect competition – implying that profits made by each firm converge to zero in the long-run.

The Bertrand model holds many of the same assumptions as Cournot, with just one adjustment – firms compete on price, not quantity. With no product differentiation, we see a stark difference in the outcome of a Bertrand competition duopoly to that of Cournot; firms make zero profit at the Nash equilibrium (the point where both firms are strategically best responding to one another’s prices). Both firms’ prices will be the same, which will be equal to their marginal costs of production. An example of two leading firms in a duopoly imitating a Bertrand model could be Coca-Cola and Pepsi. While some may argue that the soft drinks Coca-Cola produce taste a lot better than Pepsi (or vice versa), the products are effectively homogenous and are probably one of the main examples of a Bertrand duopoly. It’s harder to find examples of Cournot – not many firms compete solely in quantity.

As interesting as these outcomes are from a game theoretical perspective, what does it mean for competition in real life? Should firms in a duopoly compete on quantities to make the most profit they can? Is lack of product differentiation an extreme assumption to make when modelling market structures? These two models have received a lot of criticism for their extreme assumptions and unrealistic outcomes, and (arguably) rightfully so – not only do we live in a world where we see hundreds of variations of the same product (known as product differentiation), but there are fundamental flaws with the implications of both models. Cournot may seem unreasonable because of course most firms compete against price – but Bertrand assumes that firms can produce unlimited amounts of their respective goods, when we know that firms also face capacity constraints.

Despite this, several different models slightly adjusting each assumption of the Cournot and Bertrand have emerged, proving interesting results. A Stackelberg duopoly is an interesting model of strategic interaction involving leaders and followers, different to that of Bertrand and Cournot (which assume both agents move simultaneously).

While Stackelberg is another model of quantity competition, the idea is that a leader firm will make the first move, and the follower firm will do exactly what you’d expect – it will best respond to the leader after this.
The leader firm will consider what the second player will do, and maximises his own payoff according to what he expects the other player to do by choosing a certain quantity. In equilibrium, the follower will choose the quantity that the leader has anticipated. It’s interesting to note that with this leader and follower model, the aggregate output produced between both firms is greater than the Cournot model, and the derived price is also lower.

interesting to note that with this leader and follower model, the aggregate output produced between both firms is greater than the Cournot model, and the derived price is also lower.

This begs an interesting question: which model is better for the consumer? A large chunk of microeconomics devotes itself to welfare and whether a model’s outcome is efficient or not – and in real life, we observe that competition authorities are dedicated to ensuring fair business to consumers. Consumer surplus – a term in economics defined as the difference between the total amount that consumers are willing to pay for a good, and the total amount actually paid – is observed to be higher in Stackelberg equilibrium than it is in Cournot. However, theoretically Bertrand trumps both the Stackelberg and Cournot, with higher aggregate output, lower prices and higher consumer surplus. So clearly firms seeking higher profits might want to compete on output – but competing on price is clearly better for consumers.

Of course, it’s always important to note that these models are simplified versions of reality that are unable to explain a lot of the firm competition in real life. But, without a solid basis for strategic interactions between firms in an oligopoly, it’s difficult to understand what actually occurs in the real world. Many variations of the models I have discussed exist – economists have looked at the outcomes for when we adjust for product differentiation or imperfect information. For example, adjusting the Bertrand model to have price differentiation leads to a result where firms do make supernormal profit – albeit higher prices for consumers. But, higher prices for consumers in this case may not be a bad thing – a fundamental component of our shopping decisions is based on the brands we like or don’t like. People are usually willing to spend a bit more money on the brands they like more, whether it be due to fashion or market trends, or the implication of higher quality goods. Perhaps price isn’t everything after all – which is what these models, particularly Bertrand, insinuate!

Nonetheless, it is always interesting to look at how leaders within markets – the biggest firms within each market – will interact with one another. From a theoretical point of view within Economics, things seem simple and mathematically viable enough – but of course, it’s difficult to reflect true behaviour this way when you’re talking about firms and consumers.